WASHINGTON (Reuters) - Donald Trump's election already may be pushing up interest rates and tightening financial markets, something the Federal Reserve will have to monitor as it decides how quickly to tighten monetary policy, Fed Governor Daniel Tarullo said on Tuesday.

The Fed will not necessarily have to switch gears merely on the anticipation that a Trump administration will mount a major infrastructure spending program that increases deficits and possibly inflation, he said.

But Tarullo said recent wage growth, evidence of faster price increases and other data had already produced "a different situation" for the Fed than even a few months ago, and had re-focused discussion around the proper pace of rate increases. A radically different fiscal policy would prompt more reevaluation, Tarullo said at a Wall Street Journal CEO Council event.

"We don't want to be pushing on the brakes harder than we need to," Tarullo said. But "fiscal policy is one of the important background considerations...Give the administration time to propose its program and Congress to decide."

Trump has outlined plans for a trillion dollar investment in infrastructure, led by private sector financing, although details have yet to be fleshed out. Too much fiscal stimulus could drive inflation sharply higher, pushing the Federal Reserve into a steeper path of rate increases.

Tarullo's appearance gave some insight into the sea change the Fed may be facing in policy, its membership and its structure.

Chair Janet Yellen will appear before the Congressional Joint Economic Committee on Thursday to discuss the economy in a hearing that could give a hint of how hard and how quickly Republicans may try to overhaul the Fed's powers.

Congressional Republicans want to impose stricter oversight of the central bank, and now have a potentially friendly ear in the White House to enact legislation a Democratic president would have been likely to oppose. Those measures include proposals to make the Fed follow a mechanical policy rule, and explain to Congress if it chooses to deviate from it.

The current crop of Fed policymakers view such ideas as a threat to the independence they feel is important to keep monetary policy at arm's length from politics.

Trump, however, may be able to reshape that sensibility with new appointments to the influential board of governors, including installing his own chair when Janet Yellen's term ends in 2018.

Trump will take office with two openings already on the seven-member board, and possibly more as he makes decisions about Yellen, and Stanley Fischer, whose appointment as vice chair expires in 2018.

Governors Jerome Powell and Lael Brainard, a donor to Hillary Clinton's presidential campaign, both have appointments that last beyond Trump's term. They have not spoken publicly about their plans.

Tarullo's appointment runs until 2022, but he could face a separate sort of pressure. He has taken the lead in overseeing financial regulatory issues at the Fed. Under existing law the White House could use one of the existing openings to appoint a Vice Chair of Supervision, effectively taking his portfolio.

He would not comment on Tuesday when asked about his plans.

He did say that he hoped the new administration and Congress, as it discusses a possible rollback of financial regulations approved after the 2007 to 2009 financial crisis, keeps in mind why those rules were passed.

"We all need to keep our eyes on the reasons to strengthen regulation," Tarullo said. "Keep in the forefront of our mind the phrases moral hazard and market discipline."